The discussion revolves around finding the range of the function h(x) = sqrt(25 + (x - 3)²). Participants are exploring the implications of the function's structure and its domain.
There is an ongoing exploration of the function's properties, with some participants providing insights into the minimum values and the implications for the range. However, there is no explicit consensus on the final range yet.
Participants mention potential misunderstandings regarding the radicand being negative and the minimum values of related expressions, indicating some uncertainty in foundational concepts.
Let's get the terminology straight. You expanded (x-3)2 ; it was already factored.Codester09 said:Homework Statement
Find the range of h
Homework Equations
h(x) = sqrt(25 + (x - 3)2)
The Attempt at a Solution
I factored out the (x-3)2 and simplified to get
sqrt(x2 - 6x + 34)
The best thing, IMO, was to leave the radicand in its given form, 25 + (x-3)2. Looking at that as its own function, what is the range of this function? That will tell you a lot about the range of h(x).Codester09 said:I was trying to figure out the domain first, knowing that x2 - 6x >= -34 in order for the number inside the sqrt to be non-negative.. I don't know, maybe I'm missing something really basic here. Help? :)